Beams having cone beam geometry are known for computed tomography with multirow detectors. Reconstructing an image volume requires consideration of the cone beam geometry in the 3D image reconstruction, the cone beam geometry substantially complicating the reconstruction problem. Two different groups of image generation methods are known in principle, specifically approximate methods and exact methods:
Approximate Methods:
Approximate methods are distinguished by a high measure of practicability and flexibility. The angle of inclination of the measuring beams to the axis of rotation (cone angle) is considered in an approximate fashion, for which reason the error owing to the approximation grows with the cone angle. Starting from a certain number of detector rows, each approximate method will cause image artifacts. A distinction is made between 2D and 3D methods in the case of the approximate methods.
ASSR [1], AMPR [2] and SMPR [3] may be named as examples of the 2D method or 2D rebinning. In this case, synthetic projection data are approximated from the cone beam data, the geometry of the synthetic projection data being selected such that all the synthetic measuring beams lie in a flat plane. The object distribution in the flat plane can be reconstructed from the synthetic projection data with the aid of the conventional algorithms of 2D CT. However, with growing cone angles the approximation in the rebinning step leads relatively quickly to image artifacts.
In the case of the 3D method, filtering of the projection data and a subsequent 3D back projection are undertaken. The recorded geometry of cone beam type is taken into consideration here exactly in the back projection. Various feasible approximations are applied in the filter step. These approximation methods set forth below have in common the fact that the filtering consists of a 1D ramp filter that is aligned in the direction of the projection of the spiral tangent. The individual approximation methods differ in the processing of redundant data.
On the one hand, it is possible to average in the axial direction, as is known from [4]. Here, after the filter step the filtered projection data are back projected into the reconstruction volume such that the measured data are accumulated in weighted fashion in the process. The weights result from the axial distance of the measuring beams from the voxel to be reconstructed.
On the other hand, a reconstruction of axial slices is known from [5]. For this purpose, all the measured data that cut the image slice are used for the reconstruction. Data redundancies are considered approximately, neglecting the cone angle.
Use may be made for this purpose of conventional methods such as, for example, the Parker weighting known from [6]. The filter step includes a weighting of the projection data in accordance with the present data redundancy, followed by convolution using a 1D ramp filter. This method requires a relatively large detector surface, since the projection of the entire reconstruction slice must be included on the detector for each focal position.
Exact Methods:
A comparative study of the most important exact algorithms is to be found in [7]. Exact methods consider the recorded geometry of cone beam type in a fashion free from error both in the filter step and in the 3D back projection. These methods achieve good image results independently of the cone angle that occurs. However, they are extremely complicated and very inflexible in application. For example, a reduced pitch accompanied by the employment of data redundancies can be realized only to a limited extent, and there is no possibility at all of selecting measured data for cardiac imaging with a high time resolution.
The problem now resides in that the image quality achieved and the required computational outlay are oppositely oriented as a function of the method used. Algorithms having excellent image quality in conjunction with large cone angles, that is to say for detectors with many detector rows, are essentially intended for future scanner generations. It would be desirable to avoid exact methods, since these are complicated and inflexible.